Jeremy Corbyn has told tens of thousands of demonstrators to “defend the NHS with all of your might” at a protest march through central London.

Organised to warn that further funding cuts in the health service represent “a real risk to the safety of patients”, the event on Saturday sought to demand a fully and publicly funded NHS and social care services.

The Labour leader said to the crowd in Parliament Square: “The NHS is in crisis, in crisis because of the underfunding in social care and the people not getting the care and support they need.

“There are those waiting on trolleys and those who are desperate to get into an A&E department waiting hours for treatment. It is not the fault of the staff. It is the fault of a government who have made a political choice.”

The Labour leader, Jeremy Corbyn, waves to supporters at the rally in support of the NHS in London. Photograph: Daniel Leal-Olivas/AFP/Getty Images

Corbyn called for the budget to be unveiled by the chancellor, Philip Hammond, on Wednesday to properly fund the health service with an emphasis on social care and mental health services.

Ahead of the demonstration, the Green party spokesman Larry Sanders wrote in the Guardian: “The government tells us there isn’t enough money, but this isn’t true. We are the fifth-richest country in the world – we have the money to stop our health service turning into a humanitarian crisis, and to care for people when they grow old: in hospitals, the community and homes.”

Campaigners, medical staff and members of the public who took part in the march held up homemade banners with slogans including “We want our NHS back” and “The NHS for the needy, not the greedy”.

David Wrigley, a GP from Carnforth, Lancashire, and deputy chair of the British Medical Association council, was among the frontline staff marching under the slogan “Our NHS, No Cuts, No Closures, No Privatisation”.

He said the march was a cry for help because funding cuts had put the NHS in a desperate situation.

“Patients are not getting the care they deserve. We are a country that can afford the funding that is required,” he said.

The campaigners, who say the NHS is at breaking point, hope the march will put pressure on the government ahead of next week’s budget.

Protesters carry homemade banners during the march through central London to demand more funding for the NHS. Photograph: Neil Hall/Reuters

Wrigley said: “I guess it is also a wakeup call for Theresa May and the chancellor ... we demand they fund the NHS adequately. If the budget does not bring about any further funding increase, there would be uproar.”

The junior doctor and GP trainee Dr Jeeves Wijesuriya said the demonstration was a chance for the government to plot a new course for the NHS.

Speaking on behalf of the BMA, he told the crowd: “What is sustainable about debts that can only be paid with our patients’ health and yet still won’t be settled? Where is the transformation when the money to build new hospitals and health centres is being siphoned off to pay debts?”

Felix Ramos, 53, of Hackney, east London, said: “Many people are not going to get the help they need ... privatisation does not work. It is not going to care for the vulnerable.”

Support came from the Great British Bake Off presenter Sue Perkins, who tweeted: “Love and support to all those marching for the NHS today.”

Sue Perkins (@sueperkins)

Love & support to all those marching for the NHS today, with a special shoutout to KONP, West Cornwall Health Watch & the gang in Penzance.

A spokesman from the Department of Health said: “We are committed to the NHS, which is why we’re investing £10bn in its own plan for the future, including £4bn extra this year to transform services and improve standards of care.”